Existence of positive solutions for a critical nonlinear Schrodinger equation with vanishing or coercive potentials

Shaowei Chen

Existence of positive solutions for a critical nonlinear Schrodinger equation with vanishing or coercive potentials

Analysis of PDEs 2013-05-03 v5

Authors: Shaowei Chen

Abstract

In this paper we investigate the existence of the positive solutions for the following nonlinear Schr\"odinger equation $-\triangle u+V(x)u=K(x)|u|^{p-2}u\ {in}\ \mathbb{R}^N$ where $V(x)\sim a|x|^{-b}$ and $K(x)\sim \mu|x|^{-s}$ as $|x|\rightarrow\infty$ with $0<a,\mu<+\infty$ , $b<2,$ $b\neq0$ , $0<\frac{s}{b}<1$ and $p=2(N-2s/b)/(N-2).$

Keywords

nonlinear schrödinger equation positive solutions critical exponent vanishing potentials coercive potentials existence results elliptic equations

Cite

@article{arxiv.1302.3497,
  title  = {Existence of positive solutions for a critical nonlinear Schrodinger equation with vanishing or coercive potentials},
  author = {Shaowei Chen},
  journal= {arXiv preprint arXiv:1302.3497},
  year   = {2013}
}

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25pages

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